Income Taxes (Reconciliation of U.S Statutory Rate to Effective Tax Rate) (Details)	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Income Tax Disclosure [Abstract]
Statutory tax rate	21.00%	21.00%	21.00%
State income taxes, net of federal tax benefit	(1.60%)	(2.50%)	(0.50%)
Taxes on international activities	(0.60%)	0.80%	(0.10%)
Research credit	(3.90%)	(4.50%)	(3.10%)
Net excess income tax benefit from stock-based compensation	(3.70%)	(2.50%)	(4.20%)
Adjustments of prior period tax items	(1.30%)		0.40%
Compensation and benefits	0.60%	0.30%	0.50%
Distributable foreign earnings	4.60%
Other items, net	0.60%	1.50%	1.10%
Effective tax rate	15.70%	14.10%	15.10%